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Product Release Is the Major Contributor tok cat for the Hepatitis C Virus Helicase-catalyzed Strand Separation of Short Duplex DNA

1998; Elsevier BV; Volume: 273; Issue: 30 Linguagem: Inglês

10.1074/jbc.273.30.18906

1083-351X

David Porter, Steven A. Short, Mary H. Hanlon, Frank Preugschat, Jeanne E. Wilson, Derril H. Willard, Thomas G. Consler,

Biochemical and Molecular Research

Hepatitis C virus (HCV) helicase catalyzes the ATP-dependent strand separation of duplex RNA and DNA containing a 3′ single-stranded tail. Equilibrium and velocity sedimentation centrifugation experiments demonstrated that the enzyme was monomeric in the presence of DNA and ATP analogues. Steady-state and pre-steady-state kinetics for helicase activity were monitored by the fluorescence changes associated with strand separation of F21:HF31 that was formed from a 5′-hexachlorofluorescein-tagged 31-mer (HF31) and a complementary 3′-fluorescein-tagged 21-mer (F21).k cat for this reaction was 0.12 s−1. The fluorescence change associated with strand separation of F21:HF31 by excess enzyme and ATP was a biphasic process. The time course of the early phase (duplex unwinding) suggested only a few base pairs (∼2) were disrupted concertedly. The maximal value of the rate constant (k eff) describing the late phase of the reaction (strand separation) was 0.5 s−1, which was 4-fold greater than k cat. Release of HF31 from E·HF31 in the presence of ATP (0.21 s−1) was the major contributor tok cat. At saturating ATP and competitor DNA concentrations, the enzyme unwound 44% of F21:HF31 that was initially bound to the enzyme (low processivity). These results are consistent with a passive mechanism for strand separation of F21:HF31 by HCV helicase. Hepatitis C virus (HCV) helicase catalyzes the ATP-dependent strand separation of duplex RNA and DNA containing a 3′ single-stranded tail. Equilibrium and velocity sedimentation centrifugation experiments demonstrated that the enzyme was monomeric in the presence of DNA and ATP analogues. Steady-state and pre-steady-state kinetics for helicase activity were monitored by the fluorescence changes associated with strand separation of F21:HF31 that was formed from a 5′-hexachlorofluorescein-tagged 31-mer (HF31) and a complementary 3′-fluorescein-tagged 21-mer (F21).k cat for this reaction was 0.12 s−1. The fluorescence change associated with strand separation of F21:HF31 by excess enzyme and ATP was a biphasic process. The time course of the early phase (duplex unwinding) suggested only a few base pairs (∼2) were disrupted concertedly. The maximal value of the rate constant (k eff) describing the late phase of the reaction (strand separation) was 0.5 s−1, which was 4-fold greater than k cat. Release of HF31 from E·HF31 in the presence of ATP (0.21 s−1) was the major contributor tok cat. At saturating ATP and competitor DNA concentrations, the enzyme unwound 44% of F21:HF31 that was initially bound to the enzyme (low processivity). These results are consistent with a passive mechanism for strand separation of F21:HF31 by HCV helicase. Helicases are ubiquitous enzymes required for cellular repair, recombination, and replication (1Matson S.W. Kaiser-Rogers K.A. Annu. Rev. Biochem. 1990; 59: 289-329Crossref PubMed Scopus (335) Google Scholar, 2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar). Even though helicase activity was identified and the associated protein was purified over 20 years ago (3Abdel-Monem M. Hoffman-Berling H. Eur. J. Biochem. 1976; 65: 441-449Crossref PubMed Scopus (138) Google Scholar), the kinetic and chemical mechanism for this class of enzymes is unknown. Lohman and co-workers (4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar, 5Wong I. Chao K. Bujalowski W. Lohman T.M. J. Biol. Chem. 1992; 267: 7596-7610Abstract Full Text PDF PubMed Google Scholar, 6Amaratunga M. Lohman T.M. Biochemistry. 1993; 32: 6815-6820Crossref PubMed Scopus (99) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 8Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14565-14578Crossref PubMed Scopus (38) Google Scholar, 9Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14550-14564Crossref PubMed Scopus (60) Google Scholar, 10Bjornson K.P. Amaratunga M. Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14306-14316Crossref PubMed Scopus (94) Google Scholar, 11Bjornson K.P. Wong I. Lohman T.M. J. Mol. Biol. 1996; 263: 411-422Crossref PubMed Scopus (28) Google Scholar, 12Wong I. Moore K.J.M. Bjornson K.P. Hsieh J. Lohman T.M. Biochemistry. 1996; 35: 5726-5734Crossref PubMed Scopus (37) Google Scholar, 13Bjornson K.P. Moore K.J.M. Lohman T.M. Biochemistry. 1996; 35: 2268-2282Crossref PubMed Scopus (47) Google Scholar) have initiated an extensive effort to elucidate the mechanism of action of Escherichia coli Rep helicase. They have proposed that the catalytically active species is a dimeric form of the enzyme stabilized by DNA (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar,12Wong I. Moore K.J.M. Bjornson K.P. Hsieh J. Lohman T.M. Biochemistry. 1996; 35: 5726-5734Crossref PubMed Scopus (37) Google Scholar). The two DNA-binding sites in the catalytically active dimer unwind defined lengths of the DNA duplex by alternatively binding duplex and single-stranded DNA during the catalytic cycle (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 6Amaratunga M. Lohman T.M. Biochemistry. 1993; 32: 6815-6820Crossref PubMed Scopus (99) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 13Bjornson K.P. Moore K.J.M. Lohman T.M. Biochemistry. 1996; 35: 2268-2282Crossref PubMed Scopus (47) Google Scholar). Recently, Ali and Lohman (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar) reported that E. coli helicase II catalyzes the unwinding of defined duplexes with a step size of 4 to 5 base pairs per catalytic cycle. These results supported an active mechanism for separating double-stranded DNA in which the step size is relatively small.Our interest in helicases is based on the observation that the HCV 1The abbreviations used are: HCV, hepatitis C virus; HCV helicase, truncated domain of the NS3 protein including amino acid residues 1193–1657 of the HCV genotype 1b polyprotein; MOPS, 3-N-morpholinopropanesulfonic acid; E, helicase; E·ATP, binary complex formed from Eand ATP that may be mixtures of ATP, ADP, and inorganic phosphate;E·DNA, complex between E and DNA; andE·DNA·ATP, ternary complex of helicase, DNA, and ATP that may be mixtures of ATP, ADP, and inorganic phosphate with an undefined fraction of the base pairs in the duplex DNA disrupted; F, chemically modified fluorescein as defined in Oligos Etc. catalogue; HF, chemically modified hexachlorofluorescein as defined in Oligos Etc. catalogue; 21-mer, GAG TCA CGA CGT TGT AAA AAA; 31-mer, TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; F21, GAG TCA CGA CGT TGT AAA AAA-F; HF31, HF-TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; 42-mer, GAG TCA CGA CGT TGT AAA AAA GAG TCA CGA CGT TGT AAA AAA; HF52, HF-TTT TTT ACA ACG TCG TGA CTC TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; I, stem-loop structure, GGC CTA AGC GTA TCG CTT AGG CCG AGT CAG G;I-F, I with fluorescein on the 3′ end; AMPCPP, α,β-methyleneadenosine 5′-triphosphate; ATPγS, adenosine 5′-O-(3-thiotriphosphate); ADPPNP, 5′-adenylimidodiphosphate; bp, base pair. 1The abbreviations used are: HCV, hepatitis C virus; HCV helicase, truncated domain of the NS3 protein including amino acid residues 1193–1657 of the HCV genotype 1b polyprotein; MOPS, 3-N-morpholinopropanesulfonic acid; E, helicase; E·ATP, binary complex formed from Eand ATP that may be mixtures of ATP, ADP, and inorganic phosphate;E·DNA, complex between E and DNA; andE·DNA·ATP, ternary complex of helicase, DNA, and ATP that may be mixtures of ATP, ADP, and inorganic phosphate with an undefined fraction of the base pairs in the duplex DNA disrupted; F, chemically modified fluorescein as defined in Oligos Etc. catalogue; HF, chemically modified hexachlorofluorescein as defined in Oligos Etc. catalogue; 21-mer, GAG TCA CGA CGT TGT AAA AAA; 31-mer, TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; F21, GAG TCA CGA CGT TGT AAA AAA-F; HF31, HF-TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; 42-mer, GAG TCA CGA CGT TGT AAA AAA GAG TCA CGA CGT TGT AAA AAA; HF52, HF-TTT TTT ACA ACG TCG TGA CTC TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; I, stem-loop structure, GGC CTA AGC GTA TCG CTT AGG CCG AGT CAG G;I-F, I with fluorescein on the 3′ end; AMPCPP, α,β-methyleneadenosine 5′-triphosphate; ATPγS, adenosine 5′-O-(3-thiotriphosphate); ADPPNP, 5′-adenylimidodiphosphate; bp, base pair. genome encodes a unique helicase within the NS3 protein. Because approximately 1% of the population is infected with HCV and available therapies are effective for only a small subpopulation of these patients, an urgent medical need exists for an effective anti-HCV agent (15Choo Q.-L. Kuo G. Weiner A.J. Overby L.R. Bradley D.W. Houghton M. Science. 1989; 244: 359-362Crossref PubMed Scopus (6207) Google Scholar, 16Choo Q.-L. Richman K.H. Han J.H. Berger K. Lee C. Dong C. Gallegos C. Coit D. Medina-Selby A. Barr P.J. Weiner A.J. Bradley D.W. Kuo G. Houghton M. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 2451-2455Crossref PubMed Scopus (1524) Google Scholar, 17Magrin S. Craxi A. Fabiona C. Simonetti R.G. Fiorentino G. Marino L. Diquattro O. Di Marco V. Loiacano O. Volpes R. Almasio P. Urdea M.S. Neuwald P. Sanchez-Pescador R. Detmer J. Wilber J.C. Pagliaro L. Hepatology. 1994; 19: 273-279Crossref PubMed Scopus (226) Google Scholar). Consequently, HCV helicase is an attractive target for development of an antiviral agent for HCV.The NS3 protein of HCV has at least two enzymatic activities necessary for viral replication. The N-terminal 20 kDa of NS3 is a serine proteinase that cleaves the HCV-encoded polyprotein at four specific positions (18Grakoui A. McCourt D.W. Wychowski C. Feinstone S.M. Rice C.M. J. Virol. 1993; 67: 2832-2843Crossref PubMed Google Scholar). The C-terminal 50 kDa of NS3 has NTPase (19Suzich J.A. Tamura J.K. Palmer-Hill F. Warrener P. Grakoui A. Rice C.M. Feinstone S.M. Collett M.S. J. Virol. 1993; 67: 6152-6158Crossref PubMed Google Scholar) and RNA helicase activity (20Kim D.W. Gwack Y. Han J.H. Choe J. Biochem. Biophys. Res. Commun. 1995; 215: 160-166Crossref PubMed Scopus (289) Google Scholar). We have initiated a program to characterize the kinetic and chemical mechanism of action for the HCV helicase domain. The kinetic mechanism of the ATPase activity associated with this protein isolated from HCV genotype 1b, which is a major subtype found in both Japanese and American populations (21Bukh J. Purcell R.H. Miller R.H. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 8239-8243Crossref PubMed Scopus (267) Google Scholar), has been characterized in detail (22Preugschat F. Averett D.R. Clarke B.E. Porter D.J.T. J. Biol. Chem. 1996; 271: 24449-24457Abstract Full Text Full Text PDF PubMed Scopus (131) Google Scholar). Herein, we extend our understanding of the kinetic mechanism of the helicase activity of this protein by analysis of the strand separation reaction with fluorescently tagged duplex oligomers of defined sequences. The results with HCV helicase were consistent with a passive kinetic mechanism for DNA strand separation in which dissociation of single-stranded DNA was the major contributor tok cat.DISCUSSIONCrystal structures for helicases from Bacillus stearothermophilus (36Subramanya H.S. Bird L.E. Brannigan J.A. Wigley D.B. Nature. 1996; 384: 379-383Crossref PubMed Scopus (381) Google Scholar), HCV (37Yao N. Hesson T. Cable M. Hong Z. Kwong A.D. Le H.V. Weber P.C. Nat. Struct. Biol. 1997; 4: 463-467Crossref PubMed Scopus (420) Google Scholar), and E. coli (38Korolev S. Hsieh J. Gauss G.H. Lohman T.M. Waksman G. Cell. 1997; 90: 635-647Abstract Full Text Full Text PDF PubMed Scopus (432) Google Scholar) in the absence of divalent metal ion indicated that they were monomeric in the crystalline state. However, many helicases, such as E. coli Rep helicase (4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar), T4 helicase (32Dong F. Gogol E.P. von Hippel P.H. J. Biol. Chem. 1995; 270: 7462-7473Abstract Full Text Full Text PDF PubMed Scopus (149) Google Scholar), and DnaB helicase (39Bujalowski W. Jezewska M.J. Biochemistry. 1995; 34: 8513-8519Crossref PubMed Scopus (121) Google Scholar), appear to be oligomeric in the presence of substrates. In contrast to these helicases, HCV helicase was a monomeric protein in the presence of DNA and/or ATP analogues. Because HCV helicase contains a single DNA-binding site per monomer (22Preugschat F. Averett D.R. Clarke B.E. Porter D.J.T. J. Biol. Chem. 1996; 271: 24449-24457Abstract Full Text Full Text PDF PubMed Scopus (131) Google Scholar), these results indicated that the active form of this enzyme had a single DNA-binding site. Helicases have been proposed to unwind duplex nucleic acids by either an "active" or "passive" mechanism (7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar). The former mechanism requires that the catalytically active form of the enzyme has multiple nucleic acid-binding sites. Our finding that the active form of HCV helicase was monomeric with a single nucleic acid-binding site suggested that HCV catalyzed the unwinding of F21:HF31 by a passive mechanism.The goal of the present study was to identify the kinetic steps that contributed to k cat. Unfortunately, relating pre-steady-state data to the steady-state k catwas complicated by the processivity of the enzyme, by the step size, and by the number of base pairs broken for each ATP consumed. For helicases, a simplified scheme describing the unwinding of duplex DNA ((bp)n) bound to the enzyme is given by Equation 12. E·(bp)n→kE·(bp)n−(n/m)→kE·(bp)n−(2n/m)→k→kE·(bp)0↓k′↓k′↓k′↓k′Equation 12 In this simplified mechanism, the unwinding of double-stranded DNA with n base pairs (bp) was considered to occur sequentially in n/m steps with each unwinding event described by the pseudo first-order rate constant (k) that could be dependent on ATP concentration. Furthermore, each partially unwound duplex could dissociate from the enzyme and anneal in a process described by the rate constant k′. This model is analogous to that described by Ali and Lohman for E. coli helicase II (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). The processivity of the enzyme for DNA (P) in this model is given by Equation 13. The fraction of double-stranded DNA that was separated into single-stranded DNA by HCV helicase in a single binding event is given by Equation 14. P=kk+k′Equation 13 fractional DNA unwound=kk+k′nmEquation 14 An explicit expression for the time courses of strand separation has been derived for the simple model of Equation 12 (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). In this model, the reaction was initiated by addition of ATP and competitor DNA to E·(bp)n. Competitor DNA ensured that partially unwound (bp)n that dissociated from the enzyme annealed and did not rebind to the enzyme. The time course for strand separation of (bp)n (f(t)) is given by Equation 15. f(t)=Pnm1−∑s=0nm((k+k′)t)se−(k+k′)ts!Equation 15 The assumptions for this derivation corresponded to experimental conditions for the data of Fig. 5 where a competitor DNA was present to trap free enzyme as F21:HF31 or products dissociated from the enzyme. Numerical simulation of the time courses for strand separation of a 24-mer were made with step sizes equal to 1, 2, 3, 4, 6, 8, 12, and 24. A 24-mer was chosen over a 21-mer for these simulations because of the greater number of possible step sizes evenly divisible into 24. The simulated time courses for strand separation were biphasic in all cases except for a step size of 24 base pairs. The initial phase of the reaction using small step sizes was approximately linearly dependent on time, and the late phase of the reaction was exponentially dependent on time. The lag time for the reaction (the time defined by the intersection of the line through the lag phase data and the line drawn with the maximal slope through the exponential phase data (t l in Fig. 5)) was directly proportional to the number of steps. More importantly, the time for transition from the linear phase to the exponential phase (the portion oft l that the time course had definite curvature,t t in Fig. 5) was a decreasing fraction of the lag time of the reaction. For example, the transition from the linear phase to the exponential phase for the simulated data was 26, 46, and 62% of the lag time for step sizes of 1, 2, and 3 base pairs, respectively. The transition from the linear phase to the exponential phase for unwinding F21:HF31 and 21:HF31 (Fig. 5 and Fig. 7) was very abrupt (∼25% of the total lag time). Based on the simple model above, these results suggested that HCV helicase disrupted F21:HF31 at most several base pairs at a time. Because the free energy of hydrolysis of ATP is sufficient to break 2 to 4 base pairs (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 25Roman L.J. Kowalczykowski S.C. Biochemistry. 1989; 28: 2863-2873Crossref PubMed Scopus (147) Google Scholar), it was not unreasonable to propose a step size of 2. This would result in the efficiency for coupling the energy of ATP hydrolysis to base pair breaking of over 50%. For a step size of 2 base pairs, a lag time of approximately 1 s (average value from the data of Fig. 5 and 6), and a duplex of 21 base pairs (F21:HF31), the value for the sum ofk and k′ in Equation 12 was estimated from the simulations described above to be approximately 7.5 s−1. From the value for the sum of k and k′ (7.5 s−1), the step size (m = 2), the fraction unwound (0.44), and Equation 14, the values of k andk′ were estimated to be 7.0 s−1 and 0.5 s−1, respectively. The calculated value for dissociation of F21:HF31 in various stages of unwinding fromE·ATP·F21:HF31 (k′ = 0.5 s−1) was in good agreement with the experimental measured value of 0.84 s−1 (Fig. 3). Furthermore, the values for P, n/m, and k were used to predict the maximal value for the effective rate constant (k eff) for formation of F21 from E·ATP·F21:HF31 in the presence of a saturating concentration of enzyme (Fig. 6). The expression fork eff for conversion of (bp)n to (bp)0 derived for the model of Equation 12 with steady-state assumptions is given by Equation 16. keff≈(P−1)Pnm−1kPnm−1Equation 16 Substituting estimated values for n/m (∼11),k (7 s−1), and P (0.93) into this expression, the predicted value for k eff was 0.43 s−1, which was similar to the observed value of 0.50 s−1 (Fig. 6).Because the maximal value of the pseudo first-order rate constant for formation of F21 from F21:HF31 with excess E and ATP (0.5 s−1) was 4-fold larger than the value ofk cat (0.12 s−1), another step must contribute significantly to k cat. The dissociation rate constant of E·ATP·HF31 was 0.21 s−1, which was similar to k cat. If product dissociation and the unwinding step were the sole contributors to k cat, the calculated value ofk cat (0.15 s−1) was very close to the experimental value (0.12 s−1). Thus, the dissociation of E·HF31 was the major contributor tok cat for strand separation of F21:HF31 and the unwinding steps were minor contributors to k cat. The relevance of the interpretation of the kinetic results presented herein for F21:HF31 to normal substrate was dependent on the assumption that the tagged and untagged DNA substrates interacted similarly with the enzyme. The similarity of the selected kinetic parameters for interaction of the tagged and untagged DNA molecules with the enzyme (Table II) suggested that this assumption was valid. Helicases are ubiquitous enzymes required for cellular repair, recombination, and replication (1Matson S.W. Kaiser-Rogers K.A. Annu. Rev. Biochem. 1990; 59: 289-329Crossref PubMed Scopus (335) Google Scholar, 2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar). Even though helicase activity was identified and the associated protein was purified over 20 years ago (3Abdel-Monem M. Hoffman-Berling H. Eur. J. Biochem. 1976; 65: 441-449Crossref PubMed Scopus (138) Google Scholar), the kinetic and chemical mechanism for this class of enzymes is unknown. Lohman and co-workers (4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar, 5Wong I. Chao K. Bujalowski W. Lohman T.M. J. Biol. Chem. 1992; 267: 7596-7610Abstract Full Text PDF PubMed Google Scholar, 6Amaratunga M. Lohman T.M. Biochemistry. 1993; 32: 6815-6820Crossref PubMed Scopus (99) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 8Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14565-14578Crossref PubMed Scopus (38) Google Scholar, 9Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14550-14564Crossref PubMed Scopus (60) Google Scholar, 10Bjornson K.P. Amaratunga M. Moore K.J.M. Lohman T.M. Biochemistry. 1994; 33: 14306-14316Crossref PubMed Scopus (94) Google Scholar, 11Bjornson K.P. Wong I. Lohman T.M. J. Mol. Biol. 1996; 263: 411-422Crossref PubMed Scopus (28) Google Scholar, 12Wong I. Moore K.J.M. Bjornson K.P. Hsieh J. Lohman T.M. Biochemistry. 1996; 35: 5726-5734Crossref PubMed Scopus (37) Google Scholar, 13Bjornson K.P. Moore K.J.M. Lohman T.M. Biochemistry. 1996; 35: 2268-2282Crossref PubMed Scopus (47) Google Scholar) have initiated an extensive effort to elucidate the mechanism of action of Escherichia coli Rep helicase. They have proposed that the catalytically active species is a dimeric form of the enzyme stabilized by DNA (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar,12Wong I. Moore K.J.M. Bjornson K.P. Hsieh J. Lohman T.M. Biochemistry. 1996; 35: 5726-5734Crossref PubMed Scopus (37) Google Scholar). The two DNA-binding sites in the catalytically active dimer unwind defined lengths of the DNA duplex by alternatively binding duplex and single-stranded DNA during the catalytic cycle (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 6Amaratunga M. Lohman T.M. Biochemistry. 1993; 32: 6815-6820Crossref PubMed Scopus (99) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 13Bjornson K.P. Moore K.J.M. Lohman T.M. Biochemistry. 1996; 35: 2268-2282Crossref PubMed Scopus (47) Google Scholar). Recently, Ali and Lohman (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar) reported that E. coli helicase II catalyzes the unwinding of defined duplexes with a step size of 4 to 5 base pairs per catalytic cycle. These results supported an active mechanism for separating double-stranded DNA in which the step size is relatively small. Our interest in helicases is based on the observation that the HCV 1The abbreviations used are: HCV, hepatitis C virus; HCV helicase, truncated domain of the NS3 protein including amino acid residues 1193–1657 of the HCV genotype 1b polyprotein; MOPS, 3-N-morpholinopropanesulfonic acid; E, helicase; E·ATP, binary complex formed from Eand ATP that may be mixtures of ATP, ADP, and inorganic phosphate;E·DNA, complex between E and DNA; andE·DNA·ATP, ternary complex of helicase, DNA, and ATP that may be mixtures of ATP, ADP, and inorganic phosphate with an undefined fraction of the base pairs in the duplex DNA disrupted; F, chemically modified fluorescein as defined in Oligos Etc. catalogue; HF, chemically modified hexachlorofluorescein as defined in Oligos Etc. catalogue; 21-mer, GAG TCA CGA CGT TGT AAA AAA; 31-mer, TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; F21, GAG TCA CGA CGT TGT AAA AAA-F; HF31, HF-TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; 42-mer, GAG TCA CGA CGT TGT AAA AAA GAG TCA CGA CGT TGT AAA AAA; HF52, HF-TTT TTT ACA ACG TCG TGA CTC TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; I, stem-loop structure, GGC CTA AGC GTA TCG CTT AGG CCG AGT CAG G;I-F, I with fluorescein on the 3′ end; AMPCPP, α,β-methyleneadenosine 5′-triphosphate; ATPγS, adenosine 5′-O-(3-thiotriphosphate); ADPPNP, 5′-adenylimidodiphosphate; bp, base pair. 1The abbreviations used are: HCV, hepatitis C virus; HCV helicase, truncated domain of the NS3 protein including amino acid residues 1193–1657 of the HCV genotype 1b polyprotein; MOPS, 3-N-morpholinopropanesulfonic acid; E, helicase; E·ATP, binary complex formed from Eand ATP that may be mixtures of ATP, ADP, and inorganic phosphate;E·DNA, complex between E and DNA; andE·DNA·ATP, ternary complex of helicase, DNA, and ATP that may be mixtures of ATP, ADP, and inorganic phosphate with an undefined fraction of the base pairs in the duplex DNA disrupted; F, chemically modified fluorescein as defined in Oligos Etc. catalogue; HF, chemically modified hexachlorofluorescein as defined in Oligos Etc. catalogue; 21-mer, GAG TCA CGA CGT TGT AAA AAA; 31-mer, TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; F21, GAG TCA CGA CGT TGT AAA AAA-F; HF31, HF-TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; 42-mer, GAG TCA CGA CGT TGT AAA AAA GAG TCA CGA CGT TGT AAA AAA; HF52, HF-TTT TTT ACA ACG TCG TGA CTC TTT TTT ACA ACG TCG TGA CTC TCT CTC TCT C; I, stem-loop structure, GGC CTA AGC GTA TCG CTT AGG CCG AGT CAG G;I-F, I with fluorescein on the 3′ end; AMPCPP, α,β-methyleneadenosine 5′-triphosphate; ATPγS, adenosine 5′-O-(3-thiotriphosphate); ADPPNP, 5′-adenylimidodiphosphate; bp, base pair. genome encodes a unique helicase within the NS3 protein. Because approximately 1% of the population is infected with HCV and available therapies are effective for only a small subpopulation of these patients, an urgent medical need exists for an effective anti-HCV agent (15Choo Q.-L. Kuo G. Weiner A.J. Overby L.R. Bradley D.W. Houghton M. Science. 1989; 244: 359-362Crossref PubMed Scopus (6207) Google Scholar, 16Choo Q.-L. Richman K.H. Han J.H. Berger K. Lee C. Dong C. Gallegos C. Coit D. Medina-Selby A. Barr P.J. Weiner A.J. Bradley D.W. Kuo G. Houghton M. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 2451-2455Crossref PubMed Scopus (1524) Google Scholar, 17Magrin S. Craxi A. Fabiona C. Simonetti R.G. Fiorentino G. Marino L. Diquattro O. Di Marco V. Loiacano O. Volpes R. Almasio P. Urdea M.S. Neuwald P. Sanchez-Pescador R. Detmer J. Wilber J.C. Pagliaro L. Hepatology. 1994; 19: 273-279Crossref PubMed Scopus (226) Google Scholar). Consequently, HCV helicase is an attractive target for development of an antiviral agent for HCV. The NS3 protein of HCV has at least two enzymatic activities necessary for viral replication. The N-terminal 20 kDa of NS3 is a serine proteinase that cleaves the HCV-encoded polyprotein at four specific positions (18Grakoui A. McCourt D.W. Wychowski C. Feinstone S.M. Rice C.M. J. Virol. 1993; 67: 2832-2843Crossref PubMed Google Scholar). The C-terminal 50 kDa of NS3 has NTPase (19Suzich J.A. Tamura J.K. Palmer-Hill F. Warrener P. Grakoui A. Rice C.M. Feinstone S.M. Collett M.S. J. Virol. 1993; 67: 6152-6158Crossref PubMed Google Scholar) and RNA helicase activity (20Kim D.W. Gwack Y. Han J.H. Choe J. Biochem. Biophys. Res. Commun. 1995; 215: 160-166Crossref PubMed Scopus (289) Google Scholar). We have initiated a program to characterize the kinetic and chemical mechanism of action for the HCV helicase domain. The kinetic mechanism of the ATPase activity associated with this protein isolated from HCV genotype 1b, which is a major subtype found in both Japanese and American populations (21Bukh J. Purcell R.H. Miller R.H. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 8239-8243Crossref PubMed Scopus (267) Google Scholar), has been characterized in detail (22Preugschat F. Averett D.R. Clarke B.E. Porter D.J.T. J. Biol. Chem. 1996; 271: 24449-24457Abstract Full Text Full Text PDF PubMed Scopus (131) Google Scholar). Herein, we extend our understanding of the kinetic mechanism of the helicase activity of this protein by analysis of the strand separation reaction with fluorescently tagged duplex oligomers of defined sequences. The results with HCV helicase were consistent with a passive kinetic mechanism for DNA strand separation in which dissociation of single-stranded DNA was the major contributor tok cat. DISCUSSIONCrystal structures for helicases from Bacillus stearothermophilus (36Subramanya H.S. Bird L.E. Brannigan J.A. Wigley D.B. Nature. 1996; 384: 379-383Crossref PubMed Scopus (381) Google Scholar), HCV (37Yao N. Hesson T. Cable M. Hong Z. Kwong A.D. Le H.V. Weber P.C. Nat. Struct. Biol. 1997; 4: 463-467Crossref PubMed Scopus (420) Google Scholar), and E. coli (38Korolev S. Hsieh J. Gauss G.H. Lohman T.M. Waksman G. Cell. 1997; 90: 635-647Abstract Full Text Full Text PDF PubMed Scopus (432) Google Scholar) in the absence of divalent metal ion indicated that they were monomeric in the crystalline state. However, many helicases, such as E. coli Rep helicase (4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar), T4 helicase (32Dong F. Gogol E.P. von Hippel P.H. J. Biol. Chem. 1995; 270: 7462-7473Abstract Full Text Full Text PDF PubMed Scopus (149) Google Scholar), and DnaB helicase (39Bujalowski W. Jezewska M.J. Biochemistry. 1995; 34: 8513-8519Crossref PubMed Scopus (121) Google Scholar), appear to be oligomeric in the presence of substrates. In contrast to these helicases, HCV helicase was a monomeric protein in the presence of DNA and/or ATP analogues. Because HCV helicase contains a single DNA-binding site per monomer (22Preugschat F. Averett D.R. Clarke B.E. Porter D.J.T. J. Biol. Chem. 1996; 271: 24449-24457Abstract Full Text Full Text PDF PubMed Scopus (131) Google Scholar), these results indicated that the active form of this enzyme had a single DNA-binding site. Helicases have been proposed to unwind duplex nucleic acids by either an "active" or "passive" mechanism (7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar). The former mechanism requires that the catalytically active form of the enzyme has multiple nucleic acid-binding sites. Our finding that the active form of HCV helicase was monomeric with a single nucleic acid-binding site suggested that HCV catalyzed the unwinding of F21:HF31 by a passive mechanism.The goal of the present study was to identify the kinetic steps that contributed to k cat. Unfortunately, relating pre-steady-state data to the steady-state k catwas complicated by the processivity of the enzyme, by the step size, and by the number of base pairs broken for each ATP consumed. For helicases, a simplified scheme describing the unwinding of duplex DNA ((bp)n) bound to the enzyme is given by Equation 12. E·(bp)n→kE·(bp)n−(n/m)→kE·(bp)n−(2n/m)→k→kE·(bp)0↓k′↓k′↓k′↓k′Equation 12 In this simplified mechanism, the unwinding of double-stranded DNA with n base pairs (bp) was considered to occur sequentially in n/m steps with each unwinding event described by the pseudo first-order rate constant (k) that could be dependent on ATP concentration. Furthermore, each partially unwound duplex could dissociate from the enzyme and anneal in a process described by the rate constant k′. This model is analogous to that described by Ali and Lohman for E. coli helicase II (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). The processivity of the enzyme for DNA (P) in this model is given by Equation 13. The fraction of double-stranded DNA that was separated into single-stranded DNA by HCV helicase in a single binding event is given by Equation 14. P=kk+k′Equation 13 fractional DNA unwound=kk+k′nmEquation 14 An explicit expression for the time courses of strand separation has been derived for the simple model of Equation 12 (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). In this model, the reaction was initiated by addition of ATP and competitor DNA to E·(bp)n. Competitor DNA ensured that partially unwound (bp)n that dissociated from the enzyme annealed and did not rebind to the enzyme. The time course for strand separation of (bp)n (f(t)) is given by Equation 15. f(t)=Pnm1−∑s=0nm((k+k′)t)se−(k+k′)ts!Equation 15 The assumptions for this derivation corresponded to experimental conditions for the data of Fig. 5 where a competitor DNA was present to trap free enzyme as F21:HF31 or products dissociated from the enzyme. Numerical simulation of the time courses for strand separation of a 24-mer were made with step sizes equal to 1, 2, 3, 4, 6, 8, 12, and 24. A 24-mer was chosen over a 21-mer for these simulations because of the greater number of possible step sizes evenly divisible into 24. The simulated time courses for strand separation were biphasic in all cases except for a step size of 24 base pairs. The initial phase of the reaction using small step sizes was approximately linearly dependent on time, and the late phase of the reaction was exponentially dependent on time. The lag time for the reaction (the time defined by the intersection of the line through the lag phase data and the line drawn with the maximal slope through the exponential phase data (t l in Fig. 5)) was directly proportional to the number of steps. More importantly, the time for transition from the linear phase to the exponential phase (the portion oft l that the time course had definite curvature,t t in Fig. 5) was a decreasing fraction of the lag time of the reaction. For example, the transition from the linear phase to the exponential phase for the simulated data was 26, 46, and 62% of the lag time for step sizes of 1, 2, and 3 base pairs, respectively. The transition from the linear phase to the exponential phase for unwinding F21:HF31 and 21:HF31 (Fig. 5 and Fig. 7) was very abrupt (∼25% of the total lag time). Based on the simple model above, these results suggested that HCV helicase disrupted F21:HF31 at most several base pairs at a time. Because the free energy of hydrolysis of ATP is sufficient to break 2 to 4 base pairs (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 25Roman L.J. Kowalczykowski S.C. Biochemistry. 1989; 28: 2863-2873Crossref PubMed Scopus (147) Google Scholar), it was not unreasonable to propose a step size of 2. This would result in the efficiency for coupling the energy of ATP hydrolysis to base pair breaking of over 50%. For a step size of 2 base pairs, a lag time of approximately 1 s (average value from the data of Fig. 5 and 6), and a duplex of 21 base pairs (F21:HF31), the value for the sum ofk and k′ in Equation 12 was estimated from the simulations described above to be approximately 7.5 s−1. From the value for the sum of k and k′ (7.5 s−1), the step size (m = 2), the fraction unwound (0.44), and Equation 14, the values of k andk′ were estimated to be 7.0 s−1 and 0.5 s−1, respectively. The calculated value for dissociation of F21:HF31 in various stages of unwinding fromE·ATP·F21:HF31 (k′ = 0.5 s−1) was in good agreement with the experimental measured value of 0.84 s−1 (Fig. 3). Furthermore, the values for P, n/m, and k were used to predict the maximal value for the effective rate constant (k eff) for formation of F21 from E·ATP·F21:HF31 in the presence of a saturating concentration of enzyme (Fig. 6). The expression fork eff for conversion of (bp)n to (bp)0 derived for the model of Equation 12 with steady-state assumptions is given by Equation 16. keff≈(P−1)Pnm−1kPnm−1Equation 16 Substituting estimated values for n/m (∼11),k (7 s−1), and P (0.93) into this expression, the predicted value for k eff was 0.43 s−1, which was similar to the observed value of 0.50 s−1 (Fig. 6).Because the maximal value of the pseudo first-order rate constant for formation of F21 from F21:HF31 with excess E and ATP (0.5 s−1) was 4-fold larger than the value ofk cat (0.12 s−1), another step must contribute significantly to k cat. The dissociation rate constant of E·ATP·HF31 was 0.21 s−1, which was similar to k cat. If product dissociation and the unwinding step were the sole contributors to k cat, the calculated value ofk cat (0.15 s−1) was very close to the experimental value (0.12 s−1). Thus, the dissociation of E·HF31 was the major contributor tok cat for strand separation of F21:HF31 and the unwinding steps were minor contributors to k cat. The relevance of the interpretation of the kinetic results presented herein for F21:HF31 to normal substrate was dependent on the assumption that the tagged and untagged DNA substrates interacted similarly with the enzyme. The similarity of the selected kinetic parameters for interaction of the tagged and untagged DNA molecules with the enzyme (Table II) suggested that this assumption was valid. Crystal structures for helicases from Bacillus stearothermophilus (36Subramanya H.S. Bird L.E. Brannigan J.A. Wigley D.B. Nature. 1996; 384: 379-383Crossref PubMed Scopus (381) Google Scholar), HCV (37Yao N. Hesson T. Cable M. Hong Z. Kwong A.D. Le H.V. Weber P.C. Nat. Struct. Biol. 1997; 4: 463-467Crossref PubMed Scopus (420) Google Scholar), and E. coli (38Korolev S. Hsieh J. Gauss G.H. Lohman T.M. Waksman G. Cell. 1997; 90: 635-647Abstract Full Text Full Text PDF PubMed Scopus (432) Google Scholar) in the absence of divalent metal ion indicated that they were monomeric in the crystalline state. However, many helicases, such as E. coli Rep helicase (4Chao K. Lohman T.M. J. Mol. Biol. 1991; 221: 1165-1181Crossref PubMed Scopus (84) Google Scholar), T4 helicase (32Dong F. Gogol E.P. von Hippel P.H. J. Biol. Chem. 1995; 270: 7462-7473Abstract Full Text Full Text PDF PubMed Scopus (149) Google Scholar), and DnaB helicase (39Bujalowski W. Jezewska M.J. Biochemistry. 1995; 34: 8513-8519Crossref PubMed Scopus (121) Google Scholar), appear to be oligomeric in the presence of substrates. In contrast to these helicases, HCV helicase was a monomeric protein in the presence of DNA and/or ATP analogues. Because HCV helicase contains a single DNA-binding site per monomer (22Preugschat F. Averett D.R. Clarke B.E. Porter D.J.T. J. Biol. Chem. 1996; 271: 24449-24457Abstract Full Text Full Text PDF PubMed Scopus (131) Google Scholar), these results indicated that the active form of this enzyme had a single DNA-binding site. Helicases have been proposed to unwind duplex nucleic acids by either an "active" or "passive" mechanism (7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar). The former mechanism requires that the catalytically active form of the enzyme has multiple nucleic acid-binding sites. Our finding that the active form of HCV helicase was monomeric with a single nucleic acid-binding site suggested that HCV catalyzed the unwinding of F21:HF31 by a passive mechanism. The goal of the present study was to identify the kinetic steps that contributed to k cat. Unfortunately, relating pre-steady-state data to the steady-state k catwas complicated by the processivity of the enzyme, by the step size, and by the number of base pairs broken for each ATP consumed. For helicases, a simplified scheme describing the unwinding of duplex DNA ((bp)n) bound to the enzyme is given by Equation 12. E·(bp)n→kE·(bp)n−(n/m)→kE·(bp)n−(2n/m)→k→kE·(bp)0↓k′↓k′↓k′↓k′Equation 12 In this simplified mechanism, the unwinding of double-stranded DNA with n base pairs (bp) was considered to occur sequentially in n/m steps with each unwinding event described by the pseudo first-order rate constant (k) that could be dependent on ATP concentration. Furthermore, each partially unwound duplex could dissociate from the enzyme and anneal in a process described by the rate constant k′. This model is analogous to that described by Ali and Lohman for E. coli helicase II (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). The processivity of the enzyme for DNA (P) in this model is given by Equation 13. The fraction of double-stranded DNA that was separated into single-stranded DNA by HCV helicase in a single binding event is given by Equation 14. P=kk+k′Equation 13 fractional DNA unwound=kk+k′nmEquation 14 An explicit expression for the time courses of strand separation has been derived for the simple model of Equation 12 (14Ali J.A. Lohman T.M. Science. 1997; 275: 377-380Crossref PubMed Scopus (231) Google Scholar). In this model, the reaction was initiated by addition of ATP and competitor DNA to E·(bp)n. Competitor DNA ensured that partially unwound (bp)n that dissociated from the enzyme annealed and did not rebind to the enzyme. The time course for strand separation of (bp)n (f(t)) is given by Equation 15. f(t)=Pnm1−∑s=0nm((k+k′)t)se−(k+k′)ts!Equation 15 The assumptions for this derivation corresponded to experimental conditions for the data of Fig. 5 where a competitor DNA was present to trap free enzyme as F21:HF31 or products dissociated from the enzyme. Numerical simulation of the time courses for strand separation of a 24-mer were made with step sizes equal to 1, 2, 3, 4, 6, 8, 12, and 24. A 24-mer was chosen over a 21-mer for these simulations because of the greater number of possible step sizes evenly divisible into 24. The simulated time courses for strand separation were biphasic in all cases except for a step size of 24 base pairs. The initial phase of the reaction using small step sizes was approximately linearly dependent on time, and the late phase of the reaction was exponentially dependent on time. The lag time for the reaction (the time defined by the intersection of the line through the lag phase data and the line drawn with the maximal slope through the exponential phase data (t l in Fig. 5)) was directly proportional to the number of steps. More importantly, the time for transition from the linear phase to the exponential phase (the portion oft l that the time course had definite curvature,t t in Fig. 5) was a decreasing fraction of the lag time of the reaction. For example, the transition from the linear phase to the exponential phase for the simulated data was 26, 46, and 62% of the lag time for step sizes of 1, 2, and 3 base pairs, respectively. The transition from the linear phase to the exponential phase for unwinding F21:HF31 and 21:HF31 (Fig. 5 and Fig. 7) was very abrupt (∼25% of the total lag time). Based on the simple model above, these results suggested that HCV helicase disrupted F21:HF31 at most several base pairs at a time. Because the free energy of hydrolysis of ATP is sufficient to break 2 to 4 base pairs (2Lohman T.M. Bjornson K.P. Annu. Rev. Biochem. 1996; 65: 169-214Crossref PubMed Scopus (669) Google Scholar, 7Lohman T.M. J. Biol. Chem. 1993; 268: 2269-2272Abstract Full Text PDF PubMed Google Scholar, 25Roman L.J. Kowalczykowski S.C. Biochemistry. 1989; 28: 2863-2873Crossref PubMed Scopus (147) Google Scholar), it was not unreasonable to propose a step size of 2. This would result in the efficiency for coupling the energy of ATP hydrolysis to base pair breaking of over 50%. For a step size of 2 base pairs, a lag time of approximately 1 s (average value from the data of Fig. 5 and 6), and a duplex of 21 base pairs (F21:HF31), the value for the sum ofk and k′ in Equation 12 was estimated from the simulations described above to be approximately 7.5 s−1. From the value for the sum of k and k′ (7.5 s−1), the step size (m = 2), the fraction unwound (0.44), and Equation 14, the values of k andk′ were estimated to be 7.0 s−1 and 0.5 s−1, respectively. The calculated value for dissociation of F21:HF31 in various stages of unwinding fromE·ATP·F21:HF31 (k′ = 0.5 s−1) was in good agreement with the experimental measured value of 0.84 s−1 (Fig. 3). Furthermore, the values for P, n/m, and k were used to predict the maximal value for the effective rate constant (k eff) for formation of F21 from E·ATP·F21:HF31 in the presence of a saturating concentration of enzyme (Fig. 6). The expression fork eff for conversion of (bp)n to (bp)0 derived for the model of Equation 12 with steady-state assumptions is given by Equation 16. keff≈(P−1)Pnm−1kPnm−1Equation 16 Substituting estimated values for n/m (∼11),k (7 s−1), and P (0.93) into this expression, the predicted value for k eff was 0.43 s−1, which was similar to the observed value of 0.50 s−1 (Fig. 6). Because the maximal value of the pseudo first-order rate constant for formation of F21 from F21:HF31 with excess E and ATP (0.5 s−1) was 4-fold larger than the value ofk cat (0.12 s−1), another step must contribute significantly to k cat. The dissociation rate constant of E·ATP·HF31 was 0.21 s−1, which was similar to k cat. If product dissociation and the unwinding step were the sole contributors to k cat, the calculated value ofk cat (0.15 s−1) was very close to the experimental value (0.12 s−1). Thus, the dissociation of E·HF31 was the major contributor tok cat for strand separation of F21:HF31 and the unwinding steps were minor contributors to k cat. The relevance of the interpretation of the kinetic results presented herein for F21:HF31 to normal substrate was dependent on the assumption that the tagged and untagged DNA substrates interacted similarly with the enzyme. The similarity of the selected kinetic parameters for interaction of the tagged and untagged DNA molecules with the enzyme (Table II) suggested that this assumption was valid. We gratefully acknowledge E. Furfine for helpful discussions during the course of these studies.